Phase Correlation Functions Research Articles

Tensor-network-based variational Monte Carlo approach to the non-equilibrium steady state of open quantum systems

We introduce a novel method of efficiently simulating the non-equilibrium steady state of large many-body open quantum systems with highly non-local interactions, based on a variational Monte Carlo optimization of a matrix product operator ansatz. Our approach outperforms and offers several advantages over comparable algorithms, such as an improved scaling of the computational cost with respect to the bond dimension for periodic systems. We showcase the versatility of our approach by studying the phase diagrams and correlation functions of the dissipative quantum Ising model with collective dephasing and long-ranged power law interactions for spin chains of up to N=100 spins.

Universal scaling of the dynamic BKT transition in quenched 2D Bose gases.

The understanding of nonequilibrium dynamics in many-body quantum systems is a fundamental issue in statistical physics. Experiments that probe universal properties of these systems can address such foundational questions. In this study, we report the measurement of universal dynamics triggered by a quench from the superfluid to normal phase across the Berezinskii-Kosterlitz-Thouless transition in a two-dimensional (2D) Bose gas. We reduced the density by splitting the 2D gas in two, realizing a quench across the critical point. The subsequent relaxation dynamics were probed with matter-wave interferometry to measure the local phase fluctuations. We show that the time evolution of both the phase correlation function and vortex density obeys universal scaling laws. This conclusion is supported by classical-field simulations and interpreted by means of real-time renormalization group theory.

Observation of the Berezinskii-Kosterlitz-Thouless Transition in a Two-Dimensional Bose Gas via Matter-Wave Interferometry.

We probe local phase fluctuations of trapped two-dimensional Bose gases using matter-wave interferometry. This enables us to measure the phase correlation function, which changes from an algebraic to an exponential decay when the system crosses the Berezinskii-Kosterlitz-Thouless (BKT) transition. We determine the temperature dependence of the BKT exponent η and find the critical value η_{c}=0.17(3) for our trapped system. Furthermore, we measure the local vortex density as a function of the local phase-space density, which shows a scale-invariant behavior across the transition. Our experimental investigation is supported by MonteCarlo simulations and provides a comprehensive understanding of the BKT transition in a trapped system.

The structure of equidistant-frequency groups in the oscillation spectra of the dayside magnetosphere

The structure of natural signals (geomagnetic field disturbances in the ULF range registered at Mondy and Borok observatories) is studied for the first time by means of the APCF (amplitude and phase correlation function) method, unrelated to spectral analysis but based on analysing a specially constructed correlation function of the amplitude and phase fluctuations in the recorded signal. This method can detect the presence of a group of equidistant frequencies in the spectrum of the original signal as well as measuring the difference, Δf, of two adjacent frequencies in the group. The end product of the APCF method is a histogram of multiple Δf values. In the traditional spectral method of signal analysis, the presence in the spectrum of a peak at a certain frequency means that, in the original signal, the oscillation amplitude has a local maximum at this frequency. In the APCF “spectrum” (histogram), each peak corresponds, not to one, but to a whole group of equidistant frequencies in the original signal. The position of the peak on the horizontal axis defines, not a specific frequency, but the difference of two adjacent frequencies which is typical of the entire group.Comparison of one of the histograms for ULF disturbance records with the traditional spectrum shows that the chaotic spectrum, which is generally assumed to be noise, in reality possesses a strictly ordered structure. Most spectral peaks have been found to belong to one of many (more than 10) equidistant frequency groups. In the full spectrum, the peaks of these groups overlap forming a complex chaotic sequence.The analysis of the peaks in all the hist ograms makes it possible to conclude that the equidistant frequency groups corresponding to peaks in each histogram, are eigenfrequencies of a 2D Alfvén resonator. The existence of such a resonator in the magnetosphere, in the vicinity of the plasmapause outer edge, was earlier predicted in theoretical studies [Guglielmi, Polyakov, 1983; Leonovich, Mazur, 1987]. The APCF processing method allows this prediction to be confirmed experimentally.

Phase correlation functions: FFT vs. FHT

<p><span lang="EN-GB">The ability to process an image is a crucial skill in many measurement activities. In image processing or pattern recognition, Fast Fourier Transform (FFT) is widely used. In particular, the Phase Only Correlation (POC) method demonstrates high robustness and subpixel accuracy in pattern matching. However, there is a disadvantage in the required memory machine because of the calculation of 2D-FFT. In applications in which the use of memory is a critical element, Fast Hartley Transform (FHT) seems to be a good substitute. In this context, the use of Hartley’s transform can be of interest for apps implemented on portable systems e.g. smartphones. In this article, we present a comparison of the implementations of the phase correlation function using FFT and FHT. Particular attention is given to the analytical steps necessary to implement the POC by means of the Hartley transform.</span></p>

Resonant frequencies and spatial correlations in frustrated arrays of Josephson type nonlinear oscillators

We present a theoretical study of resonant frequencies and spatial correlations of Josephson phases in frustrated arrays of Josephson junctions. Two types of one-dimensional arrays, namely, the diamond and sawtooth chains, are discussed in detail. For these arrays in the linear regime the Josephson phase dynamics is characterized by multiband dispersion relation , and the lowest band becomes completely flat at a critical value of frustration, f = f c. In a strongly nonlinear regime such critical value of frustration determines the crossover from non-frustrated (0 < f < f c) to frustrated (f c < f < 1) regimes. The crossover is characterized by the thermodynamic spatial correlation functions of phases on vertices, , i.e. displaying the transition from long- to short-range spatial correlations. We find that higher-order correlations functions, e.g. p = 2 and p = 3, restore the long-range behavior deeply in the frustrated regime, . Monte-Carlo simulations of the thermodynamics of frustrated arrays of Josephson junctions are in good agreement with analytical results. We also outline the extension of our results to the case of kagome lattice, prototypical 2D frustrated lattice, and other higher dimensional lattices.

The effect of spectrum broadening on the O–X mode coupling due scattering of a microwave beam on plasma density fluctuations

We discuss the tunneling of quasi-optical wave beams through the evanescent region near the plasma cutoff in magnetized plasmas with density fluctuations. A model is proposed that describes the effect of a random modulation of a wave phase induced by the fluctuations along the propagation path on the efficiency of linear coupling between the ordinary and extraordinary waves in a two-dimensional geometry that suits well the toroidal magnetic systems. An analytical formula is derived that relates the averaged coupling efficiency and the phase correlation function of a random wave beam. Thresholds are found for the correlation length of the random phase and the length of the beam path, above which the density fluctuations become the dominant effect, and the importance of two-dimensional effects is shown. The analytical results are verified with full-wave numerical calculations.

Cosmological constraints from Fourier phase statistics

Most statistical inference from cosmic large-scale structure relies on two-point statistics, i.e.\ on the galaxy-galaxy correlation function (2PCF) or the power spectrum. These statistics capture the full information encoded in the Fourier amplitudes of the galaxy density field but do not describe the Fourier phases of the field. Here, we quantify the information contained in the line correlation function (LCF), a three-point Fourier phase correlation function. Using cosmological simulations, we estimate the Fisher information (at redshift $z=0$) of the 2PCF, LCF and their combination, regarding the cosmological parameters of the standard $\Lambda$CDM model, as well as a Warm Dark Matter (WDM) model and the $f(R)$ and Symmetron modified gravity models. The galaxy bias is accounted for at the level of a linear bias. The relative information of the 2PCF and the LCF depends on the survey volume, sampling density (shot noise) and the bias uncertainty. For a volume of $1h^{-3}\rm Gpc^3$, sampled with points of mean density $\bar{n} = 2\times10^{-3} h^{3}\ \rm Mpc^{-3}$ and a bias uncertainty of 13\%, the LCF improves the parameter constraints by about 20\% in the $\Lambda$CDM cosmology and potentially even more in alternative models. Finally, since a linear bias only affects the Fourier amplitudes (2PCF), but not the phases (LCF), the combination of the 2PCF and the LCF can be used to break the degeneracy between the linear bias and $\sigma_8$, present in 2-point statistics.

Phase diagram and correlation functions of the anisotropic imperfect Bose gas in d dimensions

We study an anisotropic variant of the d-dimensional imperfect Bose gas, where the asymptotic behaviour of the dispersion at vanishing momentum may differ from the standard quadratic form. The analysis reveals the key role of the shift exponent ψ governing the asymptotic behaviour of the critical temperature as a function of the chemical potential μ at . We argue that the universality classes of Bose–Einstein condensation admitted by the model may be classified according to the allowed values of ψ so that spatial dimensionality has only an indirect impact on the transition properties. We analyse the correlation function of the model and discuss its asymptotics depending on the direction. Both for the perfect and imperfect anisotropic Bose gases, the correlation function at turns out to show either exponential decay or exponentially damped oscillatory behaviour depending on the orientation of with respect to the dispersion anisotropies.

On the Effect of Small-Angle Scattering by Density Fluctuations on the Efficiency of Linear Transformation of Ordinary and Extraordinary Waves in a Toroidally Inhomogeneous Plasma

We have analyzed the efficiency of tunneling of quasi-optical wave beams through the evanescent region in the vicinity of plasma cutoff in a randomly inhomogeneous magnetoactive plasma. A new theoretical model proposed here makes it possible to study the effect of a random phase modulation induced by density fluctuations in the wave beam path on the efficiency of the linear transformation of waves in the 2D geometry corresponding to the experimental conditions for heating the overdense plasma in toroidal magnetic systems. We have derived a general analytic expression connecting the wave beam coefficient of transformation averaged over the ensemble of random wave field realizations with its phase correlation function. We have analyzed the dependence of the coefficient of transformation on the correlation length for the random phase distribution in the beam and on the traversed path length to the interaction region. The threshold value of the path length above which the fluctuations produce a dominating effect has been determined. The importance of taking into account the 2D effects has been demonstrated.

Probing cooperative force generation in collective cancer invasion

Collective cellular dynamics in the three-dimensional extracellular matrix (ECM) plays a crucial role in many physiological processes such as cancer invasion. Both chemical and mechanical signaling support cell–cell communications on a variety of length scales, leading to collective migratory behaviors. Here we conduct experiments using 3D in vitro tumor models and develop a phenomenological model in order to probe the cooperativity of force generation in the collective invasion of breast cancer cells. In our model, cell–cell communication is characterized by a single parameter that quantifies the correlation length of cellular migration cycles. We devise a stochastic reconstruction method to generate realizations of cell colonies with specific contraction phase correlation functions and correlation length a. We find that as a increases, the characteristic size of regions containing cells with similar contraction phases grows. For small a values, the large fluctuations in individual cell contraction phases smooth out the temporal fluctuations in the time-dependent deformation field in the ECM. For large a values, the periodicity of an individual cell contraction cycle is clearly manifested in the temporal variation of the overall deformation field in the ECM. Through quantitative comparisons of the simulated and experimentally measured deformation fields, we find that the correlation length for collective force generation in the breast cancer diskoid in geometrically micropatterned ECM (DIGME) system is , which is roughly twice the linear size of a single cell. One possible mechanism for this intermediate cell correlation length is the fiber-mediated stress propagation in the 3D ECM network in the DIGME system.

A method for detecting equidistant frequencies in the spectrum of a wideband signal

Examples are presented of using a signal processing technique that allows equidistant frequencies to be detected in broad-band oscillation spectra. This technique is based on analyzing the amplitude and phase correlation functions (APCF) of the oscillations. Equidistant frequencies can be detected in any broad-band spectrum based on the presence of periodic peaks related to such frequencies in APCF functions. An example of processing 1D resonator oscillations serves to show that the relationship between the eigenfrequencies in the spectrum and the APCF function peaks is similar to that between the optical grating slits and the interference line image on the screen. The proposed signal processing technique allows the difference between two adjacent frequencies of such a "grating" to be measured. The same analogy is true for a 2D resonator. In the latter case, two equidistant eigenfrequency gratings are shown to be present in the spectrum. Each grating corresponds to the eigenfrequencies of a 1D standing wave along each of the coordinates of a 2D resonator. The effect of small non-equidistance of the eigenfrequencies on the distortion and the location of the correlation function peaks is examined. The examples of processing two 1-h intervals of geomagnetic pulsation records are used to demonstrate the applicability of the APCF technique for real recorded magnetospheric oscillations.

Phase diagram and correlation functions of the two-dimensional dissipative quantum XY model

The two-dimensional dissipative quantum XY model is applicable to the quantum-critical properties of diverse experimental systems, ranging from the superconductor to insulator transitions, ferromagnetic and antiferromagnetic transitions in metals, to the loop-current order transition in the cuprates. We solve the re-expression of this model in terms of topological excitations: vortices and a variety of instantons, by renormalization group methods. The calculations explain the extraordinary properties of the model discovered in Monte-Carlo calculations: the separability of the quantum critical fluctuations (QCF) in space and time, the spatial correlation length proportional to logarithm of the temporal correlation length near the transition from disordered to the fully ordered state, and the occurrence of a phase with spatial order without temporal order. They are intimately related to the flow of the metric of time in relation to the metric of space, i.e. of the dynamical critical exponent $z$. These properties appear to be essential in understanding the strange metallic phase found in a variety of quantum-critical transitions as well as the accompanying high temperature superconductivity.

Spin frustration of a spin-1/2 Ising–Heisenberg three-leg tube as an indispensable ground for thermal entanglement

The spin-1/2 Ising–Heisenberg three-leg tube composed of the Heisenberg spin triangles mutually coupled through the Ising inter-triangle interaction is exactly solved in a zero magnetic field. By making use of the local conservation for the total spin on each Heisenberg spin triangle the model can be rigorously mapped onto a classical composite spin-chain model, which is subsequently exactly treated through the transfer-matrix method. The ground-state phase diagram, correlation functions, concurrence, Bell function, entropy and specific heat are examined in detail. It is shown that the spin frustration represents an indispensable ground for a thermal entanglement, which is quantified by the quantum concurrence. The specific heat displays diverse temperature dependences, which may include a sharp low-temperature peak mimicking a temperature-driven first-order phase transition. It is convincingly evidenced that this anomalous peak originates from massive thermal excitations from the doubly degenerate ground state towards an excited state with a high macroscopic degeneracy due to chiral degrees of freedom of the Heisenberg spin triangles.

Robust rigid registration by scanning multiple phase correlation peaks

Rigid image registration is an important image processing problem with applications in medical imaging, biometrics, image mosaicking, video stabilization, and others. A popular technique for rigid image registration consists in estimating the location of the maximum of the phase correlation function. However, multiple motions, non-rigid transformations, non-textured regions and noise introduce artefacts and spurious peaks that may confound the phase correlation method. A solution, which is proposed here, is to explore multiple peaks and estimate an error measure for each plausible transformation, in order to find the correct one. Our tests, performed with both artificially generated and real cases, show that the proposed approach can increase the probability of successful registration by 25–40% and reduce the registration error by up to 35%.

Phase correlations and quasicondensate in a two-dimensional ultracold Fermi gas

The interplay between dimensionality, coherence and interaction in superfluid Fermi gases is analyzed by the phase correlation function of the field of fermionic pairs. We calculate this phase correlation function for a two-dimensional superfluid Fermi gas with $s$-wave interactions within the Gaussian pair fluctuation formalism. The spatial behavior of the correlation function is shown to exhibit a rapid (exponential) decay at short distances and a characteristic algebraic decay at large distances, with an exponent matching that expected from Berezinskii-Kosterlitz-Thouless theory of 2D Bose superfluids. We conclude that the Gaussian pair fluctuation approximation is able to capture the physics of quasi long-range order in two-dimensional Fermi gases.

Microstructural analysis of asphalt mixtures using digital image processing techniques

In this paper, the internal microstructure of asphalt mixture is analyzed through digital image processing (DIP) of two-dimensional asphalt mixture images. A set of 12 mixtures prepared with two binders, two air voids percentages, and different recycled asphalt pavement (RAP) contents is used. First, small asphalt mixture beams of the same size of bending beam rheometer specimens are prepared for the images acquisition. Then, based on mixture volumetric properties, a three-phase material model is obtained. Finally, 2- and 3-point correlation functions of the material phases are numerically evaluated. No significant differences were observed in the microstructure and spatial distributions of aggregates, asphalt mastic, and air voids for asphalt mixtures containing up to 40% of RAP. However, an increase in auto correlation length (ACL) was found for RAP mixtures in comparison with the conventional mixtures.

Modeling Anisotropic Multiphase Heterogeneous Materials via Directional Correlation Functions: Simulations and Experimental Verification

The effective properties of heterogeneous materials critically depend on their complex microstructure. In this article, by successfully reconstructing the three-dimensional microstructure of a multiphase alloy with orientated anisotropic inclusions from two-dimensional slices, we show that such materials can be modeled by the two-point correlation functions of the inclusion phases along the three orthogonal characteristic directions of the inclusions. The reconstructions are compared to the actual microstructure obtained from high-resolution X-ray tomography experiments by quantifying certain directional cluster statistics associated with the microstructures.

Temporal correlations of elongated Bose gases at finite temperature

Temporal correlations in the harmonically trapped finite-temperature Bose gas are studied through the calculation of appropriate phase correlation functions. A wide parameter regime is covered to ascertain the role that temperature fluctuations and trap geometry play in the temporal coherence of the 1D to 3D crossover region. Bogoliubov analysis is used to establish results in the 1D and spherical limits. Formalism is then developed using the projected Gross–Pitaevskii equation to calculate correlation functions in 3D simulations of varying trap elongation and temperature.

Effect of polymer on the elasticity of surfactant membranes: A light scattering study

We have performed a dynamic light-scattering (DLS) investigation of the effect of a water-soluble polymer, polyethylene glycol (PEG), on the bending elastic modulus κ of surfactant membranes. The polymer, in concentrations ranging from 0 to 8 g/L (0 to 0.4 mM), was incorporated into the solvent of sponge phases of the sodium dodecyl sulfate (SDS)-hexanol-brine system. PEG adsorbs into the SDS membranes. The correlation functions of the polymer-doped sponge phases displayed a stretched-exponential decay, appropriately described by the Zilman-Granek (Z-G) theory for fluctuating membranes. The dynamics of the surfactant bilayers was slowed down by the addition of the polymer: Increasing PEG concentrations increase the DLS relaxation times. From the Z-G model we extracted the membrane-bending elastic modulus, as a function of polymer concentration, C(PEG) = κ increases with C(PEG), a behavior opposite to that expected from available models for the interaction between fluid membranes and adsorbing polymers. Our results suggest that the polymer penetrates to some extent the surfactant bilayers.